In order to perform CT examination with less exposure dose, an X-ray CT apparatus executing image reconstruction by the iterative approximation method has been developed in recent years. The image reconstruction by the iterative approximation method can obtain CT images with less noise even at a low dose of radiation.
In the non-patent literature 1, an iterative approximation projection data correction process that is one of the iterative approximation methods is disclosed. An iterative approximation projection data correction process is one projection data correction process that is preprocessing of image reconstruction. In an iterative approximation projection data correction process, an update formula in which a projection value of projection data is a variable is used. The update formula includes a smoothing coefficient (referred to also as a correction coefficient or a penalty item) showing a correction intensity. Also, the update formula includes weighting addition processing between adjacent elements. In an iterative approximation projection data correction process, the above update formula is used to update a projection value repeatedly. Then, for each update, a projection value obtained after the update is evaluated using a cost function. Until the cost function result becomes satisfactory, projection value update is repeated for each detection element.
The formula (1) shows a cost function to be used in conventional an iterative approximation projection data correction process.
The formula (2) shows an update formula to be used in conventional an iterative approximation projection data correction process.
                              Φ          ⁡                      (            q            )                          =                                            ∑              i                        ⁢                                                  ⁢                                                            d                  i                                ⁡                                  (                                                            y                      i                                        -                                          p                      i                                                        )                                            2                                +                      β            ⁢                                          ∑                i                                                                              ⁢                                                          ⁢                                                ∑                                      m                    ∈                                          N                      i                                                                                                                              ⁢                                                                  ⁢                                                                            w                      im                                        ⁡                                          (                                                                        p                          i                                                -                                                  p                          m                                                                    )                                                        2                                                                                        (        1        )                                          p          i                      (                          n              +              1                        )                          =                                            y              i                        +                                          β                                  ⅆ                  i                                            ⁢                              (                                                                            ∑                                              m                        ∈                                                  N                          i                          1                                                                                                                                                          ⁢                                                                                  ⁢                                                                  w                        im                                            ⁢                                              p                        m                                                  (                                                      n                            +                            1                                                    )                                                                                                      +                                                            ∑                                              m                        ∈                                                  N                          i                          2                                                                                      ⁢                                                                                  ⁢                                                                  w                        im                                            ⁢                                              p                        m                                                  (                          n                          )                                                                                                                    )                                                          1            +                                          β                                  ⅆ                  i                                            ⁢                                                ∑                                      m                    ∈                                          N                      i                                                                      ⁢                                                                  ⁢                                  w                  im                                                                                        (        2        )            
In the above formulas (1) and (2), “p” is an updated projection value, “y” is an original projection value, “β” is a smoothing coefficient, “d” is a detection characteristic value, “i” is a detection element number, “n” is a repetition number, and “w” is a weight.
Additionally, the respective formulas corresponding to the above formulas (1) and (2) are described in the non-patent literature 1. The formula (1) corresponds to the formula (9) described on p. 1274 of the non-patent literature 1. The formula (2) corresponds to the formula (11) described on p. 1274 of the non-patent literature 1.
In the present invention, although the respective formulas are described using a different form and different symbols from the non-patent literature 1 so that the explanation is made along the main aim of the invention, the contents of the above formulas (1) and (2) are the same as the respective formulas described in the non-patent literature 1.